The problem of diamagnetism, solved by Landau, continues to pose fascinating issues which have relevance even today. These issues relate to inherent quantum nature of the problem, the role of boundary and dissipation, the meaning of thermodynamic limits, and above all, the quantum–classical crossover occasioned by environment-induced decoherence. The Landau diamagnetism provides a unique paradigm for discussing these issues, the significance of which is far-reaching. Our central result connects the mean orbital magnetic moment, a thermodynamic property, with the electrical resistivity, which characterizes transport properties of material.